DW and I booked a direct flight (and paid a few hundred more) for the 4 of us (DW, DS, MiL, myself) just to be direct, and not a low cost airline, specifically to avoid problems.
That said, the best thing to do is arm yourself ahead of time with apps and tools to do flight searches. If something goes wrong and you are connecting, try to find another flight from the same carrier to get you home, and pitch it to the agent. Often then can get things fixed if you tell them what works for you (I had a Charlotte to Vancouver through Denver flight get screwed up due to a plane issue. A quick search and calling their support line and I was on the Charlotte to Seattle flight 20min later. If I didn't have the search, I would not have made the flight).
That said, the best thing to do is arm yourself ahead of time with apps and tools to do flight searches. If something goes wrong and you are connecting, try to find another flight from the same carrier to get you home, and pitch it to the agent. Often then can get things fixed if you tell them what works for you (I had a Charlotte to Vancouver through Denver flight get screwed up due to a plane issue. A quick search and calling their support line and I was on the Charlotte to Seattle flight 20min later. If I didn't have the search, I would not have made the flight).